John McTaggart was an idealist philosopher in the tradition of G. W. F. Hegel and Francis H. Bradley.

Where Hegel though the "Absolute" was progressing through time, Bradley thought "The Absolute enters into, but is itself incapable of, evolution and progress."

In McTaggart's 1908 book, The Unreality of TIme, he argued that time should not be thought of as a series of events in a past, present, and future, which he called the "A-series." In this standard view of time, an event in the future is thought to change into a present event at the moment of time we arbitrarily call "now," then slip into becoming a "past" event. McTaggart thought this perception of changing time is an illusion.

In his Mind article (Jan 1, 1908, Vol.17, p.31) with the same title, he wrote

IT doubtless seems highly paradoxical to assert that Time
is unreal, and that all statements which involve its reality are
erroneous. Such an assertion involves a far greater departure from the natural position of mankind than is involved
in the assertion of the unreality of Space or of the unreality
of Matter. So decisive a breach with that natural position is
not to be lightly accepted. And yet in all ages the belief in
the unreality of time has proved singularly attractive.

In the philosophy and religion of the East we find that
this doctrine is of cardinal importance. And in the West,
where philosophy and religion are less closely connected, we
find that the same doctrine continually recurs, both among
philosophers and among theologians. Theology never holds
itself apart from mysticism for any long period, and almost
all mysticism denies the reality of time. In philosophy,
again, time is treated as unreal by Spinoza, by Kant, by
Hegel, and by Schopenhauer. In the philosophy of the
present day the two most important movements (excluding
those which are as yet merely critical) are those which look
to Hegel and to Mr. Bradley. And both of these schools
deny the reality of time. Such a concurrence of opinion
cannot be denied to be highly significant—and is not the
less significant because the doctrine takes such different
forms, and is supported by such different arguments.

I believe that time is unreal. But I do so for reasons
which are not, I think, employed by any of the philosophers
whom I have mentioned, and I propose to explain my reasons
in this paper.

(The Unreality of Time, p. 31

McTaggart proposed a view that eliminates change, progress, and evolution. It was a "timeless" view, or as J. J. C. Smart called it, a "tenseless" view. Influenced by the Einstein-Minkowski "block universe" in which events in the future are already out there in the four-dimensional space-time, McTagggart proposed a "B-series" in which all events have unchanging descriptions.

McTaggart argued that the A series is a necessary component of any full theory of time, since change only occurs in the "A series." But he said that the "A-series" is self-contradictory and that our perception of time is, therefore, ultimately an incoherent illusion. In the standard "A-series," an event has changing properties.

"It began by being a future event. It became every moment an event in the nearer future. At last it was a present event. Then it became past, and will always remain so, though every moment it becomes further and further past. Thus we seem forced to the conclusion that all change is only a change in the characteristics imparted to events by their presence in the A series"

(The Unreality of TIme, p. 460

McTaggart claimed he could prove the incoherence of the A series. There is a contradiction in our perception of time in that all events exemplify all three of the properties of the A-series, being past, present and future. No event is all three at once, no event is past, present, and future. A single event is present, will have been future, and will become past.

McTaggart's proposed that this give rise to a vicious circle and infinite regress, because it depends upon the A-series to make sense. To distinguish the properties of being present, having been future and going to be past requires a conception of time divided into past, present and future, and hence of the A-series. He said, "Accordingly the A series has to be pre-supposed in order to account for the A series. And this is clearly a vicious circle" (p. 468).

In his McTaggart's logically consistent "B-series," every event always has a single property only, and its relationship to all other events remains timeless. It is "after" any event in its past, and "before" any event in its future.

Presentism and Perdurance Theories of Time

McTaggart's unchanging and unique character for each event lies behind modern metaphysicians who support a "presentist" or "perdurantist" theory of persistence and the idea of "temporal parts."

The great Anglo-American philosopher Alfred North Whitehead attributed the continued existence of objects from moment to moment to the intervention of God. Without a kind of continuous creation of every entity, things would fall apart. This notion can also be traced back to the American theologian Jonathan Edwards, who thought God creates every person anew from moment to moment, and is responsible for the way the world is at every instant.

Willard van Orman Quine proposed that we consider an object as existing in "stages." Quine's student, David Lewis argues that at every instant of time, every object disappears, ceases to exist, to be replaced by a very similar new entity.

He proposes temporal parts as a solution to the problem of persistence. He calls his solution "perdurance," which he distinguishes from "endurance," in which the whole entity exists at all times.
Lewis says:

Our question of overlap of worlds parallels the this-worldly problem of
identity through time; and our problem of accidental intrinsics parallels
a problem of temporary intrinsics, which is the traditional problem of
change. Let us say that something persists iff, somehow or other, it
exists at various times; this is the neutral word.

The road parts do not exactly persist. They are intrinsically different parts. The enduring entity does persist simpliciter. Matter that disappears and reappears violates the conservation laws for matter and energy..

Something perdures iff
it persists by having different temporal parts, or stages, at different times.
though no one part of it is wholly present at more than one time; whereas
it endures iff it persists by being wholly present at more than one time.
Perdurance corresponds to the way a road persists through space; part
of it is here and part of it is there, and no part is wholly present at two
different places. Endurance corresponds to the way a universal, if there
are such things, would be wholly present wherever and whenever it is
instantiated. Endurance involves overlap: the content of two different
times has the enduring thing as a common part. Perdurance does not.